Abstract

We present a new Gronwall inequality for Stieltjes integrals, which improves numerous existing results, and has a simple proof based on the quotient rule for Stieltjes integrals. As an application, we obtain uniqueness theorems for measure differential equations and nabla dynamic equations. Finally, we revisit the topic from the perspective of Stieltjes derivatives. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.